On standardness and I-cosiness

peer reviewedThe object of study of this work is the invariant characteristics of filtrations in discrete, negative time, pioneered by Vershik. We prove the equivalence between I-cosiness and standardness without using Vershik’s standardness criterion. The equivalence between I-cosiness and productness for homogeneous filtrations is further investigated by showing that the I-cosiness criterion is equivalent to Vershik’s first level criterion separately for each random variable. We also aim to derive the elementary properties of both these criteria, and to give a survey and some complements on the published and unpublished literature

Geometric methods for state space identification

The scope of identification theory is to construct algorithms for automatic model building from observed data. In these lectures we shall only discuss the case where the data are collected in one irrepetible experiment and no preparation of the experiment is possible (i.e. we cannot choose the experimenta